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ACPD

14, 29019–29055, 2014

Profiles of second- to third-order moments

of turbulent temperature fluctuations

A. Behrendt et al.

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Atmos. Chem. Phys. Discuss., 14, 29019–29055, 2014 www.atmos-chem-phys-discuss.net/14/29019/2014/ doi:10.5194/acpd-14-29019-2014

© Author(s) 2014. CC Attribution 3.0 License.

This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available.

Profiles of second- to third-order

moments of turbulent temperature

fluctuations in the convective boundary

layer: first measurements with Rotational

Raman Lidar

A. Behrendt1, V. Wulfmeyer1, E. Hammann1, S. K. Muppa1, and S. Pal2

1

University of Hohenheim, Institute of Physics and Meteorology, 70599 Stuttgart, Germany

2

University of Virginia, Department of Environmental Sciences, Charlottesville, VA 22904, USA

Received: 9 July 2014 – Accepted: 24 October 2014 – Published: 21 November 2014

Correspondence to: A. Behrendt (andreas.behrendt@uni-hohenheim.de)

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Abstract

The rotational Raman lidar of the University of Hohenheim (UHOH) measures atmo-spheric temperature profiles during daytime with high resolution (10 s, 109 m). The data contain low noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper,

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we present the first profiling of the second- to forth-order moments of turbulent tem-perature fluctuations as well as of skewness and kurtosis in the convective boundary layer (CBL) including the interfacial layer (IL). The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50◦5350.56′′N, 62750.39′′E,

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110 m a.s.l.) within one hour around local noon on 24 April 2013 during the

Inten-sive Observations Period (IOP) 6 of the HD(CP)2Observational Prototype Experiment

(HOPE), which is embedded in the German project HD(CP)2 (High-Definition Clouds

and Precipitation for advancing Climate Prediction). First, we investigated profiles of the noise variance and compared it with estimates of the statistical temperature

measure-15

ment uncertainty∆T based on Poisson statistics. The agreement confirms that photon

count numbers obtained from extrapolated analog signal intensities provide a lower es-timate of the statistical errors. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1000 m a.g.l.. Then we confirmed by

20

autocovariance and spectral analyses of the atmospheric temperature fluctuations that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the profile of the integral scale of the temperature fluctuations, which was in the range of 40 to 120 s in the CBL. Analyzing then profiles of the second-, third-, and forth-order moments, we found the largest values of all

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ments in the IL around the mean top of the CBL which was located at 1230 m a.g.l..

The maximum of the variance profile in the IL was 0.40 K2 with 0.06 and 0.08 K2 for

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14, 29019–29055, 2014

Profiles of second- to third-order moments

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nificantly different from zero inside the CBL but showed a negative peak in the IL with

a minimum of −0.72 K3 and values of 0.06 and 0.14 K3 for the sampling and noise

errors, respectively. The forth-order moment and kurtosis values throughout the CBL were quasi-normal.

1 Introduction 5

Temperature fluctuations and their vertical organization inherently govern the energy budget in the convective planetary boundary layer (CBL) by determining the vertical heat flux and modifying the interaction of vertical mean temperature gradient and tur-bulent transport (Wyngaard et al., 1971). Thus, the measurement of turtur-bulent temper-ature fluctuations and the characterizations of their statistics is essential for solving the

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turbulent energy budget closure (Stull, 1988). In-situ measurements (near the ground, on towers, or on airborne platforms) sample certain regions of the CBL within certain periods and have been used since a long time for turbulence studies. But to the best our knowledge, there are no previous observations based on a remote sensing technique suitable for this important task, i.e., resolving temperature fluctuations in high

resolu-15

tion and covering simultaneously the CBL up to the interfacial layer (IL). In this work, we demonstrate that rotational Raman lidar (RRL) (Cooney, 1972; Behrendt, 2005) can fill this gap.

By simultaneous measurements of turbulence at the land surface and in the IL, the flux divergence and other key scaling variables for sensible and latent heat entrainment

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fluxes can be determined, which is essential for the evolution of temperature and hu-midity in the CBL and for verifying turbulence parameterizations in mesoscale models (Sorbjan, 1996, 2001, 2005).

Traditionally, studies of atmospheric temperature turbulence in the CBL were per-formed with in-situ instrumentation operated on tethered balloons, helicopters, and

air-25

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instan-ACPD

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taneous profiles of turbulent fluctuations with in-situ sensor and it is difficult to identify the exact location and characteristics of the IL.

This calls for new remote sensing technologies. These instruments can be oper-ated on different platforms and can provide excellent long-term statistics, if applied from ground-based platforms. Passive remote sensing techniques, however, show

dif-5

ficulties in achieving such coverage because of their inherent limitation in both range and time resolution as well as time dependent errors in the retrievals. E.g., Kadygrov et al. (2011) published a study on temperature turbulence based on passive remote sensing techniques. The authors used a scanning microwave temperature profiler to investigate boundary layer thermal turbulence and compared the results with the

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pected−5/3-power law of Kolmogorov (1991), however, only within the lowest 200 m

layer.

In recent years, new insights in CBL turbulence were provided by studies based on active remote sensing with different types of lidar systems. Elastic backscatter lidar (Pal et al., 2010, 2013), ozone differential absorption lidar (ozone DIAL) (Senffet al.,

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1996), Doppler lidar (e.g., Wulfmeyer and Janjic, 2005; Lenschow et al., 2010), water vapor differential absorption lidar (WV DIAL) (e.g., Senff et al., 1994; Kiemle et al., 1997; Wulfmeyer, 1999a, b; Muppa et al., 2014), and water vapor Raman lidar (e.g., Wulfmeyer et al., 2010; Turner et al., 2014a, b) have been employed or a combina-tion of these techniques (e.g., Giez et al., 1996; Kiemle et al., 2007, 2011; Behrendt

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et al., 2011a; Kalthoffet al., 2013). However, so far, turbulence profiling of the key CBL variable temperature was missing.

In general, daytime measurements are more challenging than nighttime measure-ments for lidar because of the higher solar background which increases the signal noise and even prohibits measurements for most Raman lidar instruments. In order to

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14, 29019–29055, 2014

Profiles of second- to third-order moments

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Valdebenito et al., 2011), on the initiation of convection (Groenemeijer et al., 2009; Corsmeier et al., 2011), and on atmospheric stability indices (Behrendt et al., 2011; Corsmeier et al., 2011). Here, we are applying the formalism introduced by Lenschow et al. (2000) for the first time to the data of an RRL to study the extension of the variable set of lidar turbulence studies within the CBL to temperature.

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The measurements discussed here were carried out at local noon on 24 April 2013

during the Intensive Observations Period (IOP) 6 of the HD(CP)2 Observational

Pro-totype Experiment (HOPE) which is embedded in the project High-Definition Clouds

and Precipitation for advancing Climate Prediction (HD(CP)2) of the German

Re-search Ministry. The UHOH RRL was positioned during this study at 50◦53′50.56′′N,

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6◦2750.39′′E, 110 m a.s.l. near the village of Hambach in western Germany where it

performed measurements between 1 April and 31 May 2013.

This paper is organized as follows. In Sect. 2, the setup of the UHOH RRL is de-scribed briefly; more details can be found in (Hammann et al., 2014). The meteoro-logical background and turbulence measurements are presented in Sect. 3. Finally,

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conclusions are drawn in Sect. 4.

2 Setup of the UHOH RRL

The RRL technique is based on the fact that different portions of the pure rotational

backscatter spectrum show different temperature dependence. By extracting signals

our of these two portions and forming the signal ratio, one obtains a profile which, after

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calibration, yields a temperature profile of the atmosphere (see, e.g., Behrendt, 2005 for details).

A scheme of the UHOH RRL during HOPE is shown in Fig. 1. Key system pa-rameters are summarized in Table 1. As laser source, an injection-seeded frequency-tripled Nd:YAG laser (354.8 nm, 50 Hz, 10 W), model GCR 290-50 of Newport

Spectra-25

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prism (PBP) so that only the UV radiation is sent to the atmosphere. This improves eye-safety significantly compared to systems which use harmonic beam-splitters because definitely no potentially hazardous green laser light is present in the outgoing laser beam. But the main reason for using UV laser radiation for the transmitter of the UHOH RRL is that the backscatter cross section is proportional to the inverse wavelength to

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the forth power. This yields significantly stronger signals and thus lower statistical un-certainties of the measurements in the lower troposphere (see also Di Girolamo et al., 2004; Behrendt, 2005; Di Girolamo et al., 2006) when using the third harmonic instead of the second harmonic of Nd:YAG laser radiation. Behind the PBP, the laser beam

is expanded 6.5-fold in order to reduce the beam divergence to<0.2 mrad. The laser

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beam is then guided by three mirrors parallel to the optical axis of the receiving tele-scope (coaxial design) and reflected up into the atmosphere by two scanner mirrors. The same two mirrors reflect the atmospheric backscatter signals down to the receiv-ing telescope which has a primary mirror diameter of 40 cm. The scanner allows for full hemispherical scans with a scan speed of up to 10◦s−1. In the present case study, the

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scanner was pointing constantly in vertical direction. In the focus of the telescope, an iris defines the field of view. For the data shown here, we selected an iris diameter of 3 mm yielding a telescope field of view of 0.75 mrad. The light is collimated behind the iris with a convex lens and enters a polychromator which contained three channels dur-ing the discussed measurements: one channel for collectdur-ing atmospheric backscatter

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signals around the laser wavelength (elastic channel) and two channels for two signals

from different portions of the pure rotational Raman backscatter spectrum. During the

HOPE campaign, the polychromator was later extended with a water vapor Raman channel; the beamsplitter for this channel was already installed during the measure-ments discussed here. Within the polychromator, narrow-band multi-cavity interference

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bands were optimized within detailed performance simulations for measurements in the CBL in daytime (Behrendt, 2005; Radlach et al., 2008; Hammann et al., 2014). The new daytime/nighttime switch for the second rotational Raman channels (Hammann et al., 2014) was set to daytime.

3 Turbulence case study 5

3.1 Data set

The synoptic condition on 24 April 2013 was characterized by a large high-pressure system over central Europe. Because no clouds were forecasted for the HOPE region, this day was announced as Intensive Observation Period (IOP) 6 with the goal to study CBL development under clear-sky conditions. Indeed, undisturbed solar irradiance

re-10

sulted in the development of a CBL which was not affected by clouds. The time-height

plot of the particle backscatter coefficientβpar (Fig. 2) between 11:00 and 12:00 UTC

shows the CBL around local noon (11:33 UTC with a maximum solar elevation of 54◦

on this day).βpar was measured with the rotational Raman lidar technique by use of

a temperature-independent reference signal. Data below 400 m were affected by

in-15

complete geometrical overlap of the outgoing laser beam and the receiving telescope and have been excluded from this study.

The instantaneous CBL height was determined with the Haar wavelet technique which detects the strongest gradient of the aerosol backscatter signal as tracer (Pal et al., 2010, 2012; Behrendt et al., 2011a) (Fig. 2). The mean of the instantaneous

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CBL heightszi in the observation period was 1230 m a.g.l. This value is used in the

following for the normalized height scale z/zi. The standard deviation of the

instan-taneous CBL heights was 33 m; the absolute minimum and maximum were 1125 and 1323 m a.g.l., i.e., the instantaneous CBL heights were within 200 m.

The UHOH RRL temperature profile of 11:00–11:20 UTC is shown in Fig. 3 together

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Calibration of the RRL temperature data used in this study was made with these ra-diosonde data in the CBL between 400 and 1000 m a.g.l.; the RRL data above result from extrapolation of the calibration function. For the calibration, we used a 20 min

av-erage of the RRL data in order to reduce sampling effects between the two data sets.

For the statistical analysis of the turbulent temperature fluctuations, we used then this

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calibration for the one-hour RRL data set between 11:00 and 12:00 UTC. This 1 h pe-riod seems here as a good compromise to us: for much longer pepe-riods, the CBL cannot be considered as being quasi-stationary anymore while shorter periods would reduce the number of sampled thermals and thus increase the sampling errors.

The temperature profiles of RRL and radiosonde shown in Fig. 3 agree within

frac-10

tions of a kelvin in the CBL. Larger differences occur in the IL due to the different sampling methods: the mean lidar profile shows an average over 20 min while the radiosonde data sample an instantaneous profile along the sonde’s path which was determined by the drift of the sonde with the horizontal wind. In this case, the sonde needed about 5 min to reach the top of the boundary layer and was drifted by about

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1.6 km away from a vertical column above the site. Depending on the part of the ther-mal eddies in the CBL and the IL that are sampled, the radiosonde data represent thus different CBL features and are not representative for a mean profile (Weckwerth et al., 1996) which is a crucial point to be considered when using radiosonde data for scaling of turbulent properties in the CBL. Consequently, the lidar temperature data are more

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representative for a certain site.

Inside the CBL, the potential temperature (derived from the RRL temperature data with the radiosonde pressure profile) is nearly constant indicating a well-mixed CBL (Fig. 3, lower panel).zi lies approximately in the middle of the temperature inversion in the IL (Fig. 3). Figure 4 shows the temperature gradients of the radiosonde and the

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agrees with zi for both RRL profiles as determined with the Haar wavelet technique

while the height of the maximum gradient is about 60 m lower. As discussed above, the radiosonde data are not representative for a mean profile.

3.2 Turbulent temperature fluctuations

For CBL turbulence analyses, the instantaneous value of temperatureT(z) at heightz

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is separated in a slowly varying or even constant componentT(z) derived from applying a linear fit to the data typically over 30 to 60 min and the temperature fluctuationT(z)

according to

T(z)=T(z)+T(z). (1)

Figure 5 shows the time-height cross sections of temperature, potential temperature,

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and detrended temperature fluctuationsT(z) in the discussed period. For detrending,

a linear fit to the temperature time series was sufficient due to the quasi-stationary state of the CBL. One can see the positive and negative temperature fluctuations inside the CBL. In the IL, the fluctuations become larger than in heights below. Above the CBL in the free troposphere, one finds fewer structures in the temperature fluctuations and

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mostly noise.

Lidar data contain significant stochastic instrumental noise, which has to be deter-mined and for which has to be corrected in order to obtain the atmospheric fluctuation of a variable of interest. In general, the signal-to-noise ratio can be improved by aver-aging the signal in time and/or range but this in turn would of course reduce the ability

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to resolve turbulent structures. In principle, very high time resolution, i.e., the maximum allowed by the data acquisition system, is preferred in order to keep most frequencies of the turbulent fluctuations. But this is only possible as long as the derivation of tem-perature does not result in a non-linear increase of the noise errors; this noise regime should be avoided. A temporal resolution of 10 s turned out to be a good compromise

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The variance of the atmosphere x

a(z)

2

and the noise variance x

n(z)

2

of a

vari-ablexare uncorrelated. Thus, we can write (Lenschow et al., 2000)

x

m(z)

2 = x

a(z)

2 + x

n(z)

2

(2)

with x

m(z)

2

or the measured total variance. Overbars denote here and in the fol-lowing mean temporal averages over the analysis period. The separation of the

atmo-5

spheric variance from the noise contribution to the total variance can be realized by

different techniques. Most straightforward is the autocovariance method, which makes

use of the fact that atmospheric fluctuations are correlated in time while instrumen-tal noise fluctuations are uncorrelated. Further details were introduced by Lenschow et al. (2000) so that only a brief overview is given here. By calculation of the

autoco-10

variance function (ACF) of a variable and extrapolating the function to zero lag with a power-law fit, one gets the variance of the atmosphere at the extrapolated value. As the ACF at zero lag is the total variance, the instrumental noise variance is the diff er-ence of the two. Alternatively, one may calculate the power spectrum of the fluctuations

and use Kolmogorows−5/3 law within the inertial subrange in order to determine the

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noise level. We prefer the ACF method to the spectral analysis because it avoids adding

additional noise and systematic effects by conversion to the frequency space.

Figure 6 shows the ACF obtained from the measured temperature fluctuations for heights between 400 and 1230 m a.g.l., i.e., 0.3 to 1.0zi for lags from−200 to 200 s.

This interval was used for the extrapolation. The increase of the zero lag with height

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3.3 Noise errors

The resulting profiles of the total noise error of the temperature measurements

T(z)= r

T

n(z)

2

(3)

are shown in Fig. 7 together with error profiles of the photon shot noise. Both profiles are similar but it should be noted that the autocovariance technique specifies the total

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statistical error while Poisson statistics account only for the contribution of shot noise. Thus, the results of the Poisson statistics applied to the photon-count numbers provide a lower estimate for the total errors. The comparison confirms that the photon shot noise gives the main contribution and that other statistical error sources are compara-tively small.

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For calculating the noise error from the signal intensities with Poisson statistics, the following approach was made: the lidar signals are detected simultaneously in analog and photon-counting mode. As the intensities of our rotational Raman signals are too strong, the photon-counting signals are affected by deadtime effects in lower heights than about 6 km in daytime. Correction of these deadtime effects (Behrendt et al., 2004)

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is possible down to about 1.5 km. As this height limit is still too high for CBL studies, analog signals and not photon-counting signals have been used for the measurements of this study. In order to derive the statistical uncertainty of the measurements with Poisson statistics, the photon-counting signals of each 10 s profile were fitted to the analog signals in heights between about 1.5 and 3 km where both detection techniques

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were providing reliable data after deadtime correction of the photon-counting data. By extrapolation, photon counting rates were then attributed to the analog signal intensi-ties in lower altitudes. These extrapolated count rates were consequently used. The background photon-counting numbers were derived from the photon-counting signals detected from high altitudes.

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The statistical uncertainty of a signal with N photon counts according to Poisson

statistics is

N(z)= q

N(z). (4)

Error propagation then yields for the RRL temperature data (Behrendt et al., 2002)

T(z)= ∂T

∂Q

NRR2(z)

NRR1(z)

v u u u t

N

RR1(z)+

BRR1

2

(NRR1(z))

2 +

N

RR2(z)+

BRR2

2

(NRR2(z))

2 . (5)

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with N

RR1(z) and NRR2∗ (z) for the photon counts in the two rotational Raman chan-nels before background correction. NRRi(z)=NRR∗ i(z)−BRRi with i =1, 2 are the

sig-nals which are corrected for background noise per range bin BRRi. The ratio of the

two number of photon countsNRR1 and NRR2 of lower and higher rotational quantum

number transition channels

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Q=NRR2

NRR1 (6)

is the measurement parameter which yields the atmospheric temperature profile after

calibration of the system. Therefore,∂T/∂Qis provided by the temperature calibration

function.

Since the background is determined over many range bins, the statistical uncertainty

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of the background can be neglected (Behrendt et al., 2004) so that one finally gets

T(z)= ∂T

∂Q

NRR2(z)

NRR1(z)

v u u

tNRR1(z)+BRR1

(NRR1(z))

2 +

NRR2(z)+BRR2

(NRR2(z))

2 . (7)

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The background-corrected rotational Raman signals scale according to

NRRi(z)∝Ptz ηtηrA. (8)

withi =1, 2, laser powerP, measurement time∆t, range resolution∆z, transmitter and receiver efficiency ηt andηr, and receiving telescope areaA. The background counts

in each signal range bin scale in a similar way but without being influenced by powerP

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andηt, so that we get

BRRi(z)∝∆tz ηrA. (9)

One can see from Eqs. (7) to (9) that the statistical measurement uncertainty scales consequently with

Tp 1

tz ηrA

. (10)

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It is noteworthy, that increases of the laser powerP and transmitter efficiency ηt are even more effective in reducing ∆T than increases of ∆t, ∆z, ηr, or A because the former improve only the backscatter signals and do not increase the background si-multaneously like the latter. The value of the improvement obtained from increases of

P orηt, however, depends on the intensity of the background and thus on height and

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background-light conditions (see also Radlach et al., 2008; Hammann et al., 2014). The statistical uncertainties for the RRL temperature measurements at noontime shown in Fig. 7 were determined with 10 s temporal resolution and for range averaging of 109 m. The resulting error profiles for other temporal resolutions were then derived from the 10 s error profile by use of Eq. (10). The errors for other range resolutions can

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be easily obtained from Eq. (10) in a similar way.

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to about 1000 m a.g.l. With 1 min resolution,∆T is below 0.4 K up to 1000 m a.g.l. and

below 1 K up to 1530 m a.g.l. With 20 min averaging,∆T is below 0.1 and 0.3 K up to

1050 and 1770 m a.g.l., respectively.

3.4 Integral scale

Figure 8 shows the profiling of the integral scale of the temperature fluctuations. It

5

was obtained with the 2/3-power-law fit for noise correction (Lenschow et al., 2000).

Data around 0.9zi, i.e., that height region where the variance is close to zero and thus

relative errors are very large show also relative noise errors larger than 100 % for the integral scale. Consequently, these data have been excluded from the analysis. The

integral scale shows values between (40±22) s and (122±12) s in the CBL. That the

10

integral scale is significantly larger than the temporal resolution of the UHOH RRL data of 10 s confirms that the resolution of our data is high enough to resolve the turbulent temperature fluctuations including the major part of the inertial subrange throughout the CBL. The integral time scale (which can be related to a length scale provided that the mean horizontal wind speed is known) is considered as a measure of the mean

15

size of the turbulent eddies involved in the boundary layer mixing processes.

3.5 Temperature variance

What is to our best knowledge the first profile of the temperature variance of the

at-mosphere T

a(z)

2

measured with a lidar system is shown in Fig. 9; the profile starts

at about 0.3 zi and covers the whole CBL. The variance profile was calculated with

20

the 2/3-power-law-fit method, as discussed above. Between 0.3 and 0.9 zi, the

vari-ance was much smaller than in the IL. Here the values are only up to 0.058 K2 (at

982 m=0.8zi with 0.010 and 0.024 K2for the sampling and noise error, respectively).

Taken the error bars into account, one finds that the apparent minimum at 0.9zi, is not statistically significant and the one at 0.6zi only weakly significant. What remains is

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in the IL close tozi. This maximum of the variance profile was 0.40 K2with a sampling error of 0.06 and 0.08 K2 for the noise error (root-mean-square variability). Except at the surface, one expects that the temperature variance in a CBL is largest in the IL since the temporal variability is driven by entrainment caused by turbulent buoyancy-driven motions acting against the temperature inversion at the top of the CBL (e.g.,

5

Deardorff, 1974; André et al., 1978; Stull, 1988; Moeng and Wyngaard, 1989).

3.6 Third-order moment and skewness

The third-order moment (TOM) of a fluctuation is a measure of the asymmetry of the

distribution. The skewnessSis the TOM normalized by the variance to a dimensionless

parameter defined for temperature as

10

S(z)= (T′(z))

3

(T(z))2

3/2

. (11)

The normal distribution (Gaussian curve) has zero TOM and S. Positive values for

TOM andS show a right-skewed distribution where the mode is smaller than the mean.

If the mode is larger than the mean, TOM andS become negative (left-skewed

distri-bution).

15

TOM and S profiles for the atmospheric temperature fluctuations of our case are

shown in Fig. 10. Up to about 0.9 zi, TOM was not different to zero (taking the 1-σ

statistical uncertainties into account). In the IL, i.e., between 0.9 and 1.1zi, a negative

peak is found with values down to−0.72 K3with 0.06 and 0.14 K3for the sampling and

noise errors, respectively. The skewness profile shows the same characteristics. Only

20

data around 0.9 zi had to be omitted from the analysis because the variance profile

becomes close to zero here and thus division by these values yielded too large relative errors. Atzi, we found a skewness of−3.2 with 0.9 and 1.3 for the sampling and noise

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TOM and S profiles reveal interesting characteristics of the thermal plumes which

were present in the CBL in this case. We can conclude that the turbulent temperature fluctuations were not significantly skewed in the CBL; negative and positive fluctuations

were symmetric. The negative minimum in the IL shows a clear difference between

the IL and the CBL below. Between 0.9 and 1.1zi, negative and positive fluctuations

5

were not symmetric but fewer very cold fluctuations were balanced by many warm fluctuations with less difference to the mean.

Because turbulent mixing occurs in a region of positive vertical temperature gradient in the IL, the air present in the free troposphere is warmer than the air in the CBL below. Consequently, the negative peak indicates that the cold overshooting updrafts in the IL

10

were narrower in time than the downdrafts of warmer air.

Similar characteristics of the temperature TOM and skewness profiles in the CBL were discussed, e.g., by Mironov et al. (1999), Canuto et al. (2001), and Cheng et al. (2005) who compare experimental data (tank, wind tunnel, airborne in-situ), LES data, and analytical expressions.

15

3.7 Forth-order moment and kurtosis

Forth-order moment (FOM) is a measure of the steepness of the distribution. The kur-tosis is the FOM normalized by the variance to a dimensionless parameter according to

Kurtosis(z)= (T

(z))4

(T(z))2

2. (12)

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Figure 11 shows FOM and kurtosis profiles of the measured temperature fluctuations of our case. For both FOM and kurtosis, the noise errors of the data are quite large; the importance of an error analysis becomes once more obvious. Throughout the CBL, no significant differences to the normal distribution are found. While the values for the FOM are close to zero in the CBL (<0.5 K4up to 0.9zi), they appear larger in the IL, but the

5

noise error does not allow for determining exact values, zero is still within the 1-σnoise error bars. Atzi, FOM was 2.7 K4with 0.2 and 3.7 K4for the sampling and noise errors, respectively. The kurtosis atzi was 20 with 7 and 28 for the sampling and noise errors,

respectively. We conclude that the distribution of atmospheric temperature fluctuations was not significantly different to a Gaussian distribution (quasi-normal) regarding its

10

forth-order moment and kurtosis in our case.

Even if the data is here too noisy to identify non-zero FOM or kurtosis in the IL, it is interesting to note that higher values of kurtosis in the IL would reflect a situation for which a large fraction of the temperature fluctuations occurring in this region would exist due to infrequent very large deviations in temperature; the related most vigorous

15

thermals would then be capable to yield quite extreme temperature fluctuations while mixing intensively in the IL with the air of the lower free troposphere. In contrast to this, the temperature fluctuations would be more moderate (Gaussian) in the CBL below.

4 Conclusions

We have shown that rotational Raman lidar offers a remote sensing technique for the

20

analysis of turbulent temperature fluctuations within the well-developed CBL during noontime – even though the background light conditions at noon are least favorable for measurements with rotational Raman lidar. We can state that the required high tempo-ral and spatial resolution combined with low-enough statistical noise of the measured data is reached by the UHOH RRL. The data can thus be evaluated during the all time

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We have analyzed a case of the HOPE campaign. The data were collected be-tween 11:00 and 12:00 UTC on IOP 6, 24 April 2013, i.e., exactly around local noon (11:33 UTC). The UHOH RRL was located near the village of Hambach in western Germany (50◦53′50.56′′N, 6◦27′50.39′′E, 110 m a.s.l.).

A profile of the noise variance was used to estimate the statistical uncertainty∆T of

5

the temperature data with a 2/3 power law fit to the autocovariance function. A

com-parison with a ∆T profile derived with Poisson statistics demonstrated that the

sta-tistical error is mainly due to shot noise. The Haar wavelet technique was applied to

10 s profiles ofβpar and provided the mean CBL height over the observation period of

zi =1230 m a.g.l. This value is used for normalizing the height scale.

10

The results of this study give further information on turbulent temperature fluctuations and their statistics in the CBL and within the IL. The integral scale profile shows values

between (40±22) s and (122±12) s in the CBL. Thus, we can confirm that the

tempo-ral resolution of the RRL data of 10 s was sufficiently high for resolving the major part of turbulence down to the inertial subrange. The atmospheric variance profile showed

15

clearly the largest values close to zi. A maximum of the variance of the atmospheric

temperature fluctuations was found in the IL: 0.40 K2with a sampling and noise error of 0.06 and 0.08 K2, respectively. Subsequently, we also derived profiles of the third- and

forth-order moments. TOM and skewness were not significantly different to zero within

the CBL up to about 0.9zi. In the IL between 0.9 and 1.1zi, a negative minimum was

20

found with values down to−0.72 K3with 0.06 and 0.14 K3for the sampling and noise

errors, respectively. Skewness atzi was −3.2 and with 0.9 and 1.3 for the sampling

and noise errors, respectively. We conclude that the turbulent temperature fluctuations were not significantly skewed in the CBL. In contrast to this, the atmospheric temper-ature fluctuations in the IL were clearly skewed to the left (negative skewness). This

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ments but especially the FOM, the importance of an error analysis became once more obvious.

A quasi-normal FOM even when TOM is non-zero, agrees with the hypothesis of Millionshchikov (1941) which forms the basis for a large number of closure models (see Gryanik et al., 2005 for an overview). However, some recent theoretical studies,

5

measurement data, and LES data suggest that this hypothesis would not be valid for temperature in the CBL (see also see Gryanik et al., 2005 for an overview).

It is planned to extend the investigation of CBL characteristics in future studies by combining the UHOH RRL data with humidity and wind observations from water vapor DIAL (Muppa et al., 2014; Späth et al., 2014) and Doppler lidar. Furthermore, also the

10

scanning capability of the UHOH RRL will be used in future to collect data closer to the ground and even the surface layer (Behrendt et al., 2012) in order to investigate heterogeneities over different terrain.

The combination of different turbulent parameters measured by lidar – preferably, at the same atmospheric coordinates simultaneously – promises to provide further

un-15

derstanding on the important processes taking place in the CBL including the IL. For instance, till date, the key physical processes governing the IL and their relationships with other CBL properties remain unfortunately only poorly understood: they are over-simplified in empirical studies and poorly represented in the models. In consequence, more data should be evaluated to get the statistics of temperature turbulence under

20

a variety of atmospheric conditions. We believe that temperature turbulence profiling with RRL will contribute significantly to better understanding of boundary layer mete-orology in the future – not only in daytime but also at night so that the entire diurnal cycle is covered and the characteristics of temperature turbulence in different stability regimes can be observed.

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Wulfmeyer, V., Pal, S., Turner, D. D., and Wagner, E.: Can water vapour raman lidar resolve profiles of turbulent variables in the convective boundary layer?, Bound.-Lay. Meteorol., 136, 253–284, doi:10.1007/s10546-010-9494-z, 2010.

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Table 1.Overview of key parameters of the Rotational Raman Lidar of University of Hohenheim (UHOH RRL) during the measurements discussed here.

Transmitter Flash-lamp-pumped injection-seeded frequency-tripled Nd:YAG laser

Pulse energy:∼200 mJ at 354.8 nm

Repetition rate: 50 Hz

Pulse duration:∼5 ns

Receiver Diameter of primary mirror: 40 cm

Focal length: 4 m

Field of view: 0.75 mrad (selectable)

Scanner Manufactured by the NCAR, Boulder, CO, USA

Mirror coating: Protected aluminum

Scan speed: Up to 10◦s−1

Detectors Photomultiplier Tubes, Hamamatsu R7400-U02 (Elastic), R1924P (RR1+2)

Data Acquisition System 3-channel transient-recorder, LICEL GmbH, Germany

Range resolution 3.75 m in analog mode up to 30 km range

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11:00 11:15 11:30 11:45 12:00

Time, UTC

H

e

igh

t

A

G

L,

m

1800

1600

1400

1200

1000

800

600

400

Particle Backscatter Coefficient at 355 nm, 10-6/(sr m)

0 2 4 6

 

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400 600 800 1000 1200 1400 1600 1800

276 278 280 282 284 286 288 290

Temperature, K

Heigh

t, m

AGL

RRL, 1100 - 1120 UTC RS, launched at 1100 UTC

400 600 800 1000 1200 1400 1600 1800

286 288 290 292 294 296 298 300

, K

Heigh

t, m

AGL

RRL, 1100 - 1120 UTC RS, launched at 1100 UTC

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400 600 800 1000 1200 1400 1600 1800

-2 -1 0 1 2

dT/dz, K/(100 m)

Heigh

t, m

AGL

RRL, 1100 - 1200 UTC RRL , 1100 - 1120 UTC RS, launched at 1100 UTC

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11:00 11:15 11:30 11:45 12:00

Time, UTC

H

e

igh

t

A

G

L,

m

1800 1600 1400 1200 1000 800 600 400

Temperature, K

270 280 290 300

11:00 11:15 11:30 11:45 12:00

Time, UTC

H

e

igh

t

A

G

L,

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1800 1600 1400 1200 1000 800 600 400

Potential Temperature, K

280 290 300 310

11:00 11:15 11:30 11:45 12:00

Time, UTC

H

e

igh

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Temperature Fluctuations, K

-2 -1 0 1 2

Imagem

Table 1. Overview of key parameters of the Rotational Raman Lidar of University of Hohenheim (UHOH RRL) during the measurements discussed here.
Figure 1. Scheme of the UHOH RRL. The beam-steering unit (BSU) consists of two plane mirrors which scan the laser beam and receiving telescope field-of-view
Figure 2. Time-height cross section of particle backscatter coe ffi cient β par at 354.8 nm mea- mea-sured with the UHOH RRL on 24 April 2013 between 11:00 and 12:00 UTC
Figure 3. Upper panel: average temperature profile measured with the UHOH RRL on 24 April 2013 between 11:00 and 11:20 UTC and temperature profiles measured with a local  ra-diosonde launched at the lidar site at 11:00 UTC
+7

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